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<center><h1>TransitiveClosure.java</h1></center><p><br>

Below is the syntax highlighted version of <a href = "TransitiveClosure.java">TransitiveClosure.java</a>.
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<pre><tt><span class="comment">/******************************************************************************</span>
<span class="comment"> *  Compilation:  javac TransitiveClosure.java</span>
<span class="comment"> *  Execution:    java TransitiveClosure filename.txt</span>
<span class="comment"> *  Dependencies: Digraph.java DepthFirstDirectedPaths.java In.java StdOut.java</span>
<span class="comment"> *  Data files:   </span><span class="url">http://algs4.cs.princeton.edu/42digraph/tinyDG.txt</span>
<span class="comment"> *</span>
<span class="comment"> *  Compute transitive closure of a digraph and support</span>
<span class="comment"> *  reachability queries.</span>
<span class="comment"> *</span>
<span class="comment"> *  Preprocessing time: O(V(E + V)) time.</span>
<span class="comment"> *  Query time: O(1).</span>
<span class="comment"> *  Space: O(V^2).</span>
<span class="comment"> *</span>
<span class="comment"> *  % java TransitiveClosure tinyDG.txt</span>
<span class="comment"> *         0  1  2  3  4  5  6  7  8  9 10 11 12</span>
<span class="comment"> *  --------------------------------------------</span>
<span class="comment"> *    0:   T  T  T  T  T  T                     </span>
<span class="comment"> *    1:      T                                 </span>
<span class="comment"> *    2:   T  T  T  T  T  T                     </span>
<span class="comment"> *    3:   T  T  T  T  T  T                     </span>
<span class="comment"> *    4:   T  T  T  T  T  T                     </span>
<span class="comment"> *    5:   T  T  T  T  T  T                     </span>
<span class="comment"> *    6:   T  T  T  T  T  T  T        T  T  T  T</span>
<span class="comment"> *    7:   T  T  T  T  T  T  T  T  T  T  T  T  T</span>
<span class="comment"> *    8:   T  T  T  T  T  T  T  T  T  T  T  T  T</span>
<span class="comment"> *    9:   T  T  T  T  T  T           T  T  T  T</span>
<span class="comment"> *   10:   T  T  T  T  T  T           T  T  T  T</span>
<span class="comment"> *   11:   T  T  T  T  T  T           T  T  T  T</span>
<span class="comment"> *   12:   T  T  T  T  T  T           T  T  T  T</span>
<span class="comment"> *</span>
<span class="comment"> ******************************************************************************/</span>

<span class="preproc">package</span><span class="normal"> edu</span><span class="symbol">.</span><span class="normal">princeton</span><span class="symbol">.</span><span class="normal">cs</span><span class="symbol">.</span><span class="normal">algs4</span><span class="symbol">;</span>

<span class="comment">/**</span>
<span class="comment"> *  The </span><span class="keyword">&lt;tt&gt;</span><span class="comment">TransitiveClosure</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> class represents a data type for </span>
<span class="comment"> *  computing the transitive closure of a digraph.</span>
<span class="comment"> *  </span><span class="keyword">&lt;p&gt;</span>
<span class="comment"> *  This implementation runs depth-first search from each vertex.</span>
<span class="comment"> *  The constructor takes time proportional to </span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;</span><span class="comment">(</span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> + </span><span class="keyword">&lt;em&gt;</span><span class="comment">E</span><span class="keyword">&lt;/em&gt;</span><span class="comment">)</span>
<span class="comment"> *  (in the worst case) and uses space proportional to </span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;&lt;sup&gt;</span><span class="comment">2</span><span class="keyword">&lt;/sup&gt;</span><span class="comment">,</span>
<span class="comment"> *  where </span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> is the number of vertices and </span><span class="keyword">&lt;em&gt;</span><span class="comment">E</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> is the number of edges.</span>
<span class="comment"> *  </span><span class="keyword">&lt;p&gt;</span>
<span class="comment"> *  For large digraphs, you may want to consider a more sophisticated algorithm.</span>
<span class="comment"> *  </span><span class="keyword">&lt;a</span><span class="normal"> </span><span class="type">href</span><span class="normal"> </span><span class="symbol">=</span><span class="string"> "http://www.cs.hut.fi/~enu/thesis.html"</span><span class="keyword">&gt;</span><span class="comment">Nuutila</span><span class="keyword">&lt;/a&gt;</span><span class="comment"> proposes two</span>
<span class="comment"> *  algorithm for the problem (based on strong components and an interval representation)</span>
<span class="comment"> *  that runs in </span><span class="keyword">&lt;em&gt;</span><span class="comment">E</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> + </span><span class="keyword">&lt;em&gt;</span><span class="comment">V</span><span class="keyword">&lt;/em&gt;</span><span class="comment"> time on typical digraphs.</span>
<span class="comment"> *</span>
<span class="comment"> *  For additional documentation,</span>
<span class="comment"> *  see </span><span class="keyword">&lt;a</span><span class="normal"> </span><span class="type">href</span><span class="symbol">=</span><span class="string">"http://algs4.cs.princeton.edu/42digraph"</span><span class="keyword">&gt;</span><span class="comment">Section 4.2</span><span class="keyword">&lt;/a&gt;</span><span class="comment"> of</span>
<span class="comment"> *  </span><span class="keyword">&lt;i&gt;</span><span class="comment">Algorithms, 4th Edition</span><span class="keyword">&lt;/i&gt;</span><span class="comment"> by Robert Sedgewick and Kevin Wayne.</span>
<span class="comment"> *</span>
<span class="comment"> *  </span><span class="type">@author</span><span class="comment"> Robert Sedgewick</span>
<span class="comment"> *  </span><span class="type">@author</span><span class="comment"> Kevin Wayne</span>
<span class="comment"> */</span>
<span class="keyword">public</span><span class="normal"> </span><span class="keyword">class</span><span class="normal"> </span><span class="classname">TransitiveClosure</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">    </span><span class="keyword">private</span><span class="normal"> DirectedDFS</span><span class="symbol">[]</span><span class="normal"> tc</span><span class="symbol">;</span><span class="normal">  </span><span class="comment">// tc[v] = reachable from v</span>

<span class="normal">    </span><span class="comment">/**</span>
<span class="comment">     * Computes the transitive closure of the digraph </span><span class="keyword">&lt;tt&gt;</span><span class="comment">G</span><span class="keyword">&lt;/tt&gt;</span><span class="comment">.</span>
<span class="comment">     * </span><span class="type">@param</span><span class="comment"> G the digraph</span>
<span class="comment">     */</span>
<span class="normal">    </span><span class="keyword">public</span><span class="normal"> </span><span class="function">TransitiveClosure</span><span class="symbol">(</span><span class="usertype">Digraph</span><span class="normal"> G</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        tc </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> DirectedDFS</span><span class="symbol">[</span><span class="normal">G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">()];</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            tc</span><span class="symbol">[</span><span class="normal">v</span><span class="symbol">]</span><span class="normal"> </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">DirectedDFS</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">,</span><span class="normal"> v</span><span class="symbol">);</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="normal">    </span><span class="comment">/**</span>
<span class="comment">     * Is there a directed path from vertex </span><span class="keyword">&lt;tt&gt;</span><span class="comment">v</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> to vertex </span><span class="keyword">&lt;tt&gt;</span><span class="comment">w</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> in the digraph?</span>
<span class="comment">     * </span><span class="type">@param</span><span class="comment"> v the source vertex</span>
<span class="comment">     * </span><span class="type">@param</span><span class="comment"> w the target vertex</span>
<span class="comment">     * </span><span class="type">@return</span><span class="comment"> </span><span class="keyword">&lt;tt&gt;</span><span class="comment">true</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> if there is a directed path from </span><span class="keyword">&lt;tt&gt;</span><span class="comment">v</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> to </span><span class="keyword">&lt;tt&gt;</span><span class="comment">w</span><span class="keyword">&lt;/tt&gt;</span><span class="comment">,</span>
<span class="comment">     *    </span><span class="keyword">&lt;tt&gt;</span><span class="comment">false</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> otherwise</span>
<span class="comment">     */</span>
<span class="normal">    </span><span class="keyword">public</span><span class="normal"> </span><span class="type">boolean</span><span class="normal"> </span><span class="function">reachable</span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v</span><span class="symbol">,</span><span class="normal"> </span><span class="type">int</span><span class="normal"> w</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        </span><span class="keyword">return</span><span class="normal"> tc</span><span class="symbol">[</span><span class="normal">v</span><span class="symbol">].</span><span class="function">marked</span><span class="symbol">(</span><span class="normal">w</span><span class="symbol">);</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="normal">    </span><span class="comment">/**</span>
<span class="comment">     * Unit tests the </span><span class="keyword">&lt;tt&gt;</span><span class="comment">TransitiveClosure</span><span class="keyword">&lt;/tt&gt;</span><span class="comment"> data type.</span>
<span class="comment">     */</span>
<span class="normal">    </span><span class="keyword">public</span><span class="normal"> </span><span class="keyword">static</span><span class="normal"> </span><span class="type">void</span><span class="normal"> </span><span class="function">main</span><span class="symbol">(</span><span class="normal">String</span><span class="symbol">[]</span><span class="normal"> args</span><span class="symbol">)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">        </span><span class="usertype">In</span><span class="normal"> in </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">In</span><span class="symbol">(</span><span class="normal">args</span><span class="symbol">[</span><span class="number">0</span><span class="symbol">]);</span>
<span class="normal">        </span><span class="usertype">Digraph</span><span class="normal"> G </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">Digraph</span><span class="symbol">(</span><span class="normal">in</span><span class="symbol">);</span>

<span class="normal">        </span><span class="usertype">TransitiveClosure</span><span class="normal"> tc </span><span class="symbol">=</span><span class="normal"> </span><span class="keyword">new</span><span class="normal"> </span><span class="function">TransitiveClosure</span><span class="symbol">(</span><span class="normal">G</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// print header</span>
<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">print</span><span class="symbol">(</span><span class="string">"     "</span><span class="symbol">);</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span>
<span class="normal">            StdOut</span><span class="symbol">.</span><span class="function">printf</span><span class="symbol">(</span><span class="string">"%3d"</span><span class="symbol">,</span><span class="normal"> v</span><span class="symbol">);</span>
<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">();</span>
<span class="normal">        StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">(</span><span class="string">"--------------------------------------------"</span><span class="symbol">);</span>

<span class="normal">        </span><span class="comment">// print transitive closure</span>
<span class="normal">        </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> v </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> v </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> v</span><span class="symbol">++)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">            StdOut</span><span class="symbol">.</span><span class="function">printf</span><span class="symbol">(</span><span class="string">"%3d: "</span><span class="symbol">,</span><span class="normal"> v</span><span class="symbol">);</span>
<span class="normal">            </span><span class="keyword">for</span><span class="normal"> </span><span class="symbol">(</span><span class="type">int</span><span class="normal"> w </span><span class="symbol">=</span><span class="normal"> </span><span class="number">0</span><span class="symbol">;</span><span class="normal"> w </span><span class="symbol">&lt;</span><span class="normal"> G</span><span class="symbol">.</span><span class="function">V</span><span class="symbol">();</span><span class="normal"> w</span><span class="symbol">++)</span><span class="normal"> </span><span class="cbracket">{</span>
<span class="normal">                </span><span class="keyword">if</span><span class="normal"> </span><span class="symbol">(</span><span class="normal">tc</span><span class="symbol">.</span><span class="function">reachable</span><span class="symbol">(</span><span class="normal">v</span><span class="symbol">,</span><span class="normal"> w</span><span class="symbol">))</span><span class="normal"> StdOut</span><span class="symbol">.</span><span class="function">printf</span><span class="symbol">(</span><span class="string">"  T"</span><span class="symbol">);</span>
<span class="normal">                </span><span class="keyword">else</span><span class="normal">                    StdOut</span><span class="symbol">.</span><span class="function">printf</span><span class="symbol">(</span><span class="string">"   "</span><span class="symbol">);</span>
<span class="normal">            </span><span class="cbracket">}</span>
<span class="normal">            StdOut</span><span class="symbol">.</span><span class="function">println</span><span class="symbol">();</span>
<span class="normal">        </span><span class="cbracket">}</span>
<span class="normal">    </span><span class="cbracket">}</span>

<span class="cbracket">}</span>

<span class="comment">/******************************************************************************</span>
<span class="comment"> *  Copyright 2002-2015, Robert Sedgewick and Kevin Wayne.</span>
<span class="comment"> *</span>
<span class="comment"> *  This file is part of algs4.jar, which accompanies the textbook</span>
<span class="comment"> *</span>
<span class="comment"> *      Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,</span>
<span class="comment"> *      Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.</span>
<span class="comment"> *      </span><span class="url">http://algs4.cs.princeton.edu</span>
<span class="comment"> *</span>
<span class="comment"> *</span>
<span class="comment"> *  algs4.jar is free software: you can redistribute it and/or modify</span>
<span class="comment"> *  it under the terms of the GNU General Public License as published by</span>
<span class="comment"> *  the Free Software Foundation, either version 3 of the License, or</span>
<span class="comment"> *  (at your option) any later version.</span>
<span class="comment"> *</span>
<span class="comment"> *  algs4.jar is distributed in the hope that it will be useful,</span>
<span class="comment"> *  but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<span class="comment"> *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span>
<span class="comment"> *  GNU General Public License for more details.</span>
<span class="comment"> *</span>
<span class="comment"> *  You should have received a copy of the GNU General Public License</span>
<span class="comment"> *  along with algs4.jar.  If not, see </span><span class="url">http://www.gnu.org/licenses.</span>
<span class="comment"> ******************************************************************************/</span>
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Last updated: Mon Mar 21 10:51:08 EDT 2016.
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